Question: Solve the Initial value problem:

.

Express your answer in the form , where has no constant term.

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Attempt at the question:

First of all I checked the terms to see if they were exact and they are not. I took the integral with respect to for which is the first part of the equation and it came out to be . Afterwards I took the partial with respect to y of that integral we just got which was: . I now would equate both these equations together and would cancel terms. The result gives me . So, my equation . But my question now is, how do I solve using the initial values since my equation has both terms and ?

Thanks for everyone who contributes!